Solve for $x$ and $y$ using elimination. ${-x+3y = 4}$ ${-2x+5y = 4}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-2$ ${2x-6y = -8}$ $-2x+5y = 4$ Add the top and bottom equations together. $-y = -4$ $\dfrac{-y}{{-1}} = \dfrac{-4}{{-1}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-x+3y = 4}\thinspace$ to find $x$ ${-x + 3}{(4)}{= 4}$ $-x+12 = 4$ $-x+12{-12} = 4{-12}$ $-x = -8$ $\dfrac{-x}{{-1}} = \dfrac{-8}{{-1}}$ ${x = 8}$ You can also plug ${y = 4}$ into $\thinspace {-2x+5y = 4}\thinspace$ and get the same answer for $x$ : ${-2x + 5}{(4)}{= 4}$ ${x = 8}$